Exotic Quantum Phases and Criticality

这笔拨款支持强相互作用凝聚态系统的理论研究。在这些系统中，固体中的电子受到它们强烈的相互作用和无序状态的极大影响。对这类系统的理论研究需要新的理论方法。实验和初步的理论研究揭示了物质的丰富的新的和奇异的状态。虽然这项研究是现代凝聚态物理的核心，但其结果可能会影响我们对纳米物理和量子计算的理解。智力价值随着规律性的增强，对“新型”电子材料的新的、更精细的实验正在揭示-并加剧-与基于费米液体理论的固体物理标准范式的戏剧性偏离。在d-壳层过渡金属氧化物、f-壳层稀土化合物以及一些有机分子晶体中的偏差尤其显著。这种可怕的情况表明，有必要和迫切地为强相互作用的多费米子系统开发一种新的理论范式。目前的理论进步是由相互作用电子的2D和3D模型的新重构推动的，其中包括Z2和U(1)规范理论和玻色子-涡旋对偶变换等。出现了许多奇特的量子相和相变，包括具有拓扑有序的二维和三维Mott绝缘体，二维“临界”自旋液体绝缘体，二维非费米液体导体和新的解禁闭量子临界。理论和实验之间的融合一直是断断续续的，但前景越来越光明。在这里，我们的目的是开发一种新的方法来研究2D量子系统，这种方法将规范理论与Chern-Simons统计变形相结合，以帮助推动这一努力。1.提高对拓扑有序自旋液体绝缘体，特别是二维Kagome反铁磁体的认识，以及在超冷原子系统中立方光学晶格上实现三维U(1)自旋液体的可能性。在2d内探索“临界”代数自旋液体，并在铜赝隙和有机Mott绝缘体k(BEDT)2X.3中进行实验。通过使合子和涡旋费米化，发展了一种描述二维非费米液体导体的方法，以解决在铜酸盐和MOGe超导薄膜中看到的“奇怪的金属”。将我们最近对“去受限量子临界性”的理解扩展到包括巡回电子系统，并着眼于重费米子量子临界性。将一维(玻色子)Luttinger液体中点接触输运的理论分析推广到二维超导薄膜之间的约瑟夫森弱连接，并面对现有的纳米线实验。广泛的影响基于最近在碳纳米管中观察到的透明Luttinger液体物理的成功，很明显，我们在理解复杂的多电子系统方面的任何理论进展都将有助于刚刚起步的纳米物理工作。更具体地说，如果使用这种相来执行“无消相干”量子计算的提议得到实现，那么理解和控制具有拓扑顺序的奇异量子相的努力将是至关重要的。

This grant supports theoretical research on strongly interacting condensed matter systems. These systems are ones in which electrons in solids are dramatically affected by their strong interactions and their disordered state. The theoretical study of these type of systems requires new theoretical methods. Experimental, and preliminary theoretical, studies have revealed a wealth of new and exotic states of matter. While the research is at the core of modern condensed matter physics, the results may impact our understanding of nanophysics and quantum computation.Intellectual MeritWith increasing regularity, new and more refined experiments on "novel" electronic materialsare revealing - and sharpening - dramatic deviations from the standard paradigm of solid state physics based on Fermi liquid theory. Deviations are especially striking in the d-shell transition metal oxides, the f-shell rare earth compounds as well as some organic molecular crystals. This dire situation points to the need and urgency of developing a new theoretical paradigm for strongly interacting many-fermion systems. Current theoretical advances are being fueled by novel reformulations of 2d and 3d models of interacting electrons involving Z2 and U(1) gauge theories and boson-vortex duality transformations, among others. The existence of a slew of exotic quantum phases and transitions have emerged including, 2d and 3d Mott insulators with topological order, 2d "critical" spin liquid insulators, 2d non-Fermi liquid conductors and novel deconfined quantum criticality. Convergence between theoryand experiment has been intermitant, but with increasing promise. Here, the intention is to exploit a new approach to 2d quantum systems which combines gauge theory with Chern-Simons statistics transmutation, to help push this effort forward. Progress should be possible in the following areas:1. Advancing our understanding of topologically ordered spin liquid insulators, especially the 2d Kagome antiferromagnet, and the possible realization of the 3d U(1) spin liquid on a cubicoptical lattice in ultracold atomic systems.2. Exploring "critical" algebraic spin liquids in 2d, and confronting experiments in the cupratepseudo-gap and in the organic Mott insulator k(BEDT)2X.3. Developing a description of 2d Non-Fermi liquid conductors by fermionizing holons and vortices, to address the "strange metals" seen in the cuprates and MoGe supeconducting films.4. Extending our recent understanding of "deconfined quantum criticality" to include itinerantelectron systems, with an eye towards heavy fermion quantum criticality.5. Generalizing the theoretical analysis of transport through a point contact in a 1d (bosonic)Luttinger liquid, to a Josephson weak link between 2d superconducting films, and confrontingexisting nano-wire experiments.Broader ImpactBased on recent successes such as the observation of clear Luttinger liquid physics in carbon nanotubes, it is clear that any theoretical advances in our understanding of complex many-electron systems will help the fledgling nanophysics effort. More specifically, the effort to understand and control exotic quantum phases with topological order will be critical if the proposal to employ such phases to perform "decoherence free" quantum computation will ever be fulfilled.